integral of (sin(2/x))/(x^2)

解答

\int \frac{sin ( \frac{2}{x} )}{x ^{2}} d x

\frac{1}{2} cos (\frac{2}{x}) + C

求解步骤

\int \frac{sin ( \frac{2}{x} )}{x ^{2}} d x

使用换元积分法

= \int - \frac{sin ( u )}{2} d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2} \cdot \int sin (u) d u

使用积分常见定则:

\int sin (u) d u = - cos (u)

= - \frac{1}{2} (- cos (u))

u = \frac{2}{x}

代回

= - \frac{1}{2} (- cos (\frac{2}{x}))

化简

= \frac{1}{2} cos (\frac{2}{x})

解答补常数

= \frac{1}{2} cos (\frac{2}{x}) + C

\frac{d}{d x} (\frac{5}{3} x^{2} y^{- 2})

\int \frac{2}{x ^{2} + 9} d x

n = 0 \sum \infty \frac{n}{1 + n ^{2}}

t an g e n t f (x) = \frac{2}{x ^{2}}, (7, \frac{2}{49})

\frac{d}{d x} (ln (3 x^{2} + 1))